Toshkent 2022 The 3rd

AXBOROT TEXNOLOGIYALARI VA KOMMUNIKATSIYALARINI RIVOJLANTIRISH VAZIRLIGI
MUHAMMAD AL-XORAZMIY NOMIDAGI TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI
LABORATORIYA ISHI №3

Bajardi: Abduqodirov Sarvar

Tekshirdi: Sabirov Karimjon


TOSHKENT 2022


The 3^rd laboratory work

1. 
   Write a integral representation of coefficients of Fourier series of the given tabular function;
   

2. 
   Calculate integrals of the represented coefficients using integration formulas.
   

2. 
   Find a leading harmonic of digital signals based on Fourier series;
   

clc;
clear all;
close all;
N=2;
a(1)=191/2048;
c(1)=abs(a(1));
for n=1:N
a(n+1)=-50/2*sin(52.5*pi*n/28);
b(n+1)=50/2*(1-cos(52.5*pi*n/28));
for i=1:7
a(n+1)=a(n+1)+50/2^(9-i)*(sin(50*(2*i+1)*pi*n/200)-sin(50*(2*i-1)*pi*n/200));
b(n+1)=b(n+1)+50/2^(9-i)*(cos(50*(2*i+1)*pi*n/200)-cos(50*(2*i-1)*pi*n/200));
end
a(n+1)=1/(pi*n)*a(n+1);
b(n+1)=-1/(pi*n)*b(n+1);
c(n+1)=sqrt(a(n+1)^2+b(n+1)^2);
end
disp(c);
ANSWER:
warning: function ./demo.m shadows a core library function
0.093262 5.146076 1.173786

2. 
   Construct mathematical models for a linear model using the least square method;
   

clc;
clear all;
close all;
t=[0 50 100 150 200 250 300 350 400]
f=[0 50/256 50/128 50/64 50/32 50/16 50/8 50/4 50/2]
A=[sum(t) length(t);
sum(t.*t) sum(t)]
A1=[sum(f) length(t);
sum(t.*f) sum(t)]
A2=[sum(t) sum(f);
sum(t.*t) sum(t.*f)]
a=det(A1)/det(A)
b=det(A2)/det(A)
ANSWER:
t =

0 50 100 150 200 250 300 350 400

f =

Columns 1 through 7:

0.00000 0.19531 0.39062 0.78125 1.56250 3.12500 6.25000

Columns 8 and 9:

12.50000 25.00000

A =

1800 9
510000 1800

A1 =

49.80469 9.00000
17509.76562 1800.00000

A2 =

1800.00000 49.80469
510000.00000 17509.76562
a = 0.050326
b = -4.5313

Y=AX+B
Y = 0.050326X – 4.5313

2. 
   Construct mathematical models for a quadratic model using the least square method;